Election Laws, Disproportionality and Median Correspondence: Implications … · 2018. 7. 11. · 2 Consider Arend Lijphart’s judgement: ‘This is an important practical conclusion

B.J.Pol.S.30, 383–411 Copyright 2000 Cambridge University PressPrinted in the United Kingdom

Election Laws, Disproportionality and MedianCorrespondence: Implications for Two Visionsof Democracy

G. BINGHAM POWELL JR AND GEORG S. VANBERG*

Comparative studies of election rules and legislative representation have focused intensively onvote–seat disproportionality as an indication of poor representation. Beginning with citizens’preferences, rather than votes, has important advantages and is especially more appropriate fora majoritarian vision of democracy. We analyse the effect of election rules on both vote–seatcorrespondence and median left–right correspondence in seventy elections in seventeencountries. We show theoretically the stringent conditions necessary to reduce vote–seatdisproportionality in high threshold systems and empirically their high variance (and higherlevels) of distortion. Although good median correspondence could be created, in theory, undera wide range of electoral systems, our empirical results suggest that proportional representation(PR) systems tend to outperform single-member district (SMD) systems by this criterion also.

The impact of election law on the (dis)proportionality of representation of votersin legislatures has been intensively studied. Empirically, it is quite clear andwidely accepted that election laws greatly influence the manner in whichcitizens’ votes at the polls are converted into seats in the legislature.1 Morespecifically, electoral systems with some form of proportional representationrules, large districts and low legal thresholds convert votes into seats quiteaccurately. Electoral systems with higher thresholds, smaller districts and,especially, plurality rules often create substantial distortion in the proportional-ity of vote–seat representation. Scholars concerned about representation indemocracies have used vote–seat disproportionality as one measure of thequality of representation, concluding that low threshold proportional represen-tation (PR) election laws generally provide better representation.2 Presumably,disproportionality is a relevant measure in this context because vote–seat

* Department of Political Science, University of Rochester; and Department of Political Science,Florida State University, respectively. We are grateful to John Carey, Arend Lijphart, Gail McElroy,Rein Taagepera, Albert Weale and the anonymous reviewers for theJournal for their extremelyhelpful comments and suggestions.

1 Michael Gallagher, ‘Proportionality, Disproportionality, and Electoral Systems’,ElectoralStudies, 10 (1991), 33–51; Arend Lijphart,Electoral Systems and Party Systems: A Study ofTwenty-Seven Democracies, 1945–1990(New York: Oxford University Press, 1994); Douglas Rae,The Political Consequences of Electoral Laws(New Haven, Conn.: Yale University Press, 1967);Rein Taagepera and Matthew S. Shugart,Seats and Votes: The Effects and Determinants of ElectoralSystems(New Haven, Conn.: Yale University Press, 1989).

2 Consider Arend Lijphart’s judgement: ‘This is an important practical conclusion because thereis well-nigh universal agreement that electoral proportionality is a major goal of electoral systemsand a major criterion by which they should be judged. For many PR supporters, proportionality is

384 POWELL AND VANBERG

distributions represent the most tangible and easily quantifiable evidenceavailable about the preferences of the electorate and their reflection in thelegislature. Votes are the closest approximation to ‘revealed preferences’ for thepublic as a whole.

While we respect both the meaningfulness of the vote and the progress thathas been made in studying the effect of election laws on the vote–seatrelationship, we think that important parts of the problem of electoral law andrepresentation have been neglected. First, despite great progress, aspects of thecausal connection between electoral systems and vote–seat disproportionalityremain obscure. In particular, the problem that votes are translated into seats atthe district level, while disproportionality is conceived of as a national-levelphenomenon, has not received sufficient attention. Secondly, focusing on therelationship between seats and votes assumes (at least implicitly) that all we canknow, or need to know, about citizens’ preferences in a discussion ofrepresentation is captured by the distribution of citizens’ votes. But the votedistribution itself is strongly affected by the alternatives that are offered tocitizens (i.e., by the party system) and by citizens’ perceptions of thosealternatives. The policy positions of the parties in turn depend at least in parton the incentives that electoral laws generate for voters and politicians. If wethink the point of elections is to convert citizens’ preferences into representationthrough the medium of votes and the rules for aggregating those votes, thenideally we should begin with preferences, not votes, in our analysis.

This last point can be of particular importance because the majoritarian visionof democracy that underlies much justification of plurality, single-memberdistrict rules (which are often characterized by high vote–seat distortion)explicitly denies the normative importance of vote–seat disproportionality assuch. In this vision, the purpose of legislative elections is not to represent therange of citizen preferences or to convert votes into seats accurately. Rather, itis to reduce the diversity of citizen preferences in such a way as to create alegislative majority for a party that represents the policy preferences of a citizenmajority.3 The point of elections in this vision is to allow voters to choosedecisively the government itself, leading presumably to responsiveness andaccountability.4 As we shall illustrate it is quite possible, even plausible, to findclose correspondence of citizen and legislative majorities in conjunction withgreat vote–seat distortion. Even if we accepted the authenticity of the votedistribution as an indication of citizen preferences, vote–seat disproportionality

(F’note continued)

a goal in and of itself – virtually synonymous with electoral justice – but is also regarded as animportant means for minority representation’ (Lijphart,Electoral Systems and Party Systems, p.140).

3 John D. Huber and G. Bingham Powell Jr, ‘Congruence between Citizens and Policymakersin Two Visions of Liberal Democracy’,World Politics, 46 (1994), 291–326; Arend Lijphart,Democracies: Patterns of Majoritarian and Consensus Government(New Haven, Conn.: YaleUniversity Press, 1984).

4 Dennis Mueller, ‘Choosing a Constitution in East Europe: Lessons from Public Choice’,Journal of Comparative Economics, 15 (1991), 325–48; G. Bingham Powell Jr, ‘ConstitutionalDesign and Citizen Electoral Control’,Journal of Theoretical Politics, 1 (1989), 107–30.

Election Laws, Disproportionality and Median Correspondence385

as such would therefore be inappropriate for normative evaluations of electoralsystems from a majoritarian point of view.

We address these concerns in two stages. First, we investigate the causalconnection between electoral law and disproportionality, taking particularaccount of the national–district aggregation problem. Then, we move analysisof the performance of election laws in creating desirable representation ofcitizen preferences in the primary law-authorizing body – the nationallegislature – beyond the vote–seat measures of disproportionality. Our tool fordoing so is the left–right scale, which makes it possible to compare thepolicy-positions of citizens with the policy-positions of the parties that representthem in a kind of ‘super’ issue dimension.

The latter analysis requires us to accept the meaningfulness of the left–rightscale as a measure of preference. We recognize that this assumption is notalways justified, and particularly that the reduction of multiple dimensions intothis single one is more problematic in some situations than others. Butsubstantial work on public opinion suggests that the left–right scale position isa reasonable summary of citizens’ views in the context of national politicaldebate in most of these countries.5 Our analysis requires only that the distancesbetween left–right positions be comparable across times and countries, not thatthe substantive positions be similar (see also the more detailed discussion in thepenultimate section below).

Despite the inevitable concerns about the left–right metric, it has two criticaladvantages. First, this approach allows us begin analysis with a direct measureof citizen preferences rather than with votes. Secondly, unlike measures ofdisproportionality, which are shaped by the exclusion of parties at any policyposition, such analysis can focus directly on the normative concern of themajoritarian vision that citizens and their representatives share the samepreference majorities. In this article, we shall analyse the correspondence oflegislative and citizen medians on the left–right scale, which captures thismajoritarian concern. In a single-issue dimension, the position of the median isprivileged because it is the only policy position that cannot be defeated byanother position in a head-on vote. The further from the citizen median thelegislative median is located, the larger the citizen majority that would preferan alternative. While this is the critical property for majoritarians, it is obviouslyrelevant for proponents of other visions of representation as well. Althoughnon-majoritarians, who desire to see the full range of citizen preferences in the

5 Matthew J. Gabel and John D. Huber, ‘Putting Parties in Their Place: Inferring Party Left–RightIdeological Positions from Manifestos’ Data’ (Ann Arbor: unpublished paper, 1998); John D. Huber,‘Values and Partisanship in Left–Right Orientations: Measuring Ideology’,European Journal ofPolitical Research, 17 (1989), 599–621; Ronald Inglehart, ‘The Changing Structure of PoliticalCleavages in Western Society’, in Russell Dalton, Scott C. Flanagan and Paul Allen Beck, eds,Electoral Change in Advanced Industrial Societies: Realignment or Dealignment(Princeton, NJ:Princeton University Press, 1984), pp. 25–69; Ronald Inglehart and Hans-Dieter Klingemann, ‘PartyIdentification, Ideological Preference, and the Left–Right Dimension among Western Mass Publics,’in Ian Budgeet al., eds,Party Identification and Beyond(London: John Wiley, 1976), pp. 243–73.


legislature, may feel that the correspondence of the medians is not sufficient forgood representation, they should still wish the legislative body to be centred onthe citizen distribution, which requires good correspondence of the medians.

ELECTORAL LAW AND DISPROPORTIONALITY

Electoral Systems: The Effective Threshold

Before moving into the heart of our argument, it will be necessary to take a shortdetour into the problems of measuring electoral laws and disproportionality. Thereason for this is fairly straightforward. Electoral laws vary on numerousdimensions; many of these dimensions have an impact on how difficult it willbe for a party to gain seats in the assembly. For example, the German electoralsystem features a 5 per cent minimum threshold for representation, which tendsto increase disproportionality as small parties are left out of the legislature. Otherelectoral systems, for example Norway before 1989, do not employ legalthresholds, but have relatively small district magnitudes or other features thatcan also make entry more difficult for small parties. We expect theoretically thatwhere entry is more difficult, there is greater likelihood of disproportionality inrepresentation. To study systematically the relationship between electoral lawand disproportionality, it would be desirable to find a measure that combinesthese various aspects of electoral systems in such a way as to make meaningfulcomparison across systems possible. Fortunately, we can take advantage of aconcept that has been widely employed in the literature on electoral systems forthis purpose: Arend Lijphart’s notion of an ‘effective threshold’.6 The purposeof this measure is to take the various aspects of an electoral system, and toconvert them into an equivalent (fictitious) legal threshold that would haveapproximately the same effect on difficulty of entry to the legislature as theelectoral law under consideration.

In particular, the effective threshold aims to capture two properties of anelectoral system. The first is its ‘upper threshold,’ i.e. an approximation of themaximum vote share a party or candidate could receive under the most adversecircumstances without winning a seat. The second is the ‘lower threshold’, i.e.an approximation of the minimum vote share that could win a party a seat underthe most favourable circumstances. If there is no stipulated national minimum,Lijphart calculates the average of the ‘upper’ and ‘lower’ threshold numbers tobe the effective threshold of an electoral system. The exact formula is given by:7

Teff550%

M 1 11

50%

2M,

whereM denotes the average district magnitude.

6 Lijphart, Electoral Systems, p. 267 The crucial ingredients in calculating the upper and lower thresholds are the average district

magnitude, any existing legal thresholds, and certain assumptions about the number of competingparties. For a precise statement of the derivation of the effective threshold, see Lijphart,ElectoralSystems, pp. 26f.


If a national minimum threshold exists and if it exceeds this average, Lijphartuses it as the effective threshold. One difficulty with this measure is that forsingle-member, plurality-rule (SMD) systems, it yields an effective thresholdof 50 per cent, which is equivalent to the upper threshold. Therefore we followthe convention of assigning a value of 35 per cent to these systems.8 The highestthreshold for any non-single member district system in our sample is only about13 per cent (France in 1986).9 Intuitively, the effective threshold thus providesus with a rough estimate of the difficulty of gaining seats in a given electoralsystem. The higher the effective threshold, the more support a party must secure,on average, in order to gain seats. As is intuitive, and as the formula makes clear,the effective threshold falls with increases in district magnitude.

Effective Threshold and Disproportionality

That disproportionality rises with increases in the effective threshold has beenwell documented. In our sample, consisting of seventy elections in seventeencountries between 1977 and 1993, we find similar results. The particulardisproportionality measure we use in our analysis is Michael Gallagher’s leastsquares index.10 The data are presented graphically in Figure 1, a scatter plotof disproportionality by Lijphart’s effective threshold measure. The SMDsystems (due to their assigned effective threshold of 35) are grouped togetherat the right side of the graph, while the PR systems are positioned on the leftside. Even to the unaided eye, the result is unambiguous: empirically, at least,higher thresholds do seem to entail higher disproportionality scores.11The moredifficult an electoral system makes it for parties to gain representation in thelegislature, the greater the divergence, on average, between vote and seat sharesthat parties obtain.12

8 Lijphart, Electoral Systems, p. 279 The Appendix Table A1, available on the internet version of this article, shows the effective

thresholds for each election in our sample.10 Gallagher, ‘Proportionality, Disproportionality, and Electoral Systems’. The least squares index

is calculated as the square root of

1

2 On

i 5 1

(vi 2 Si)2,

where vi and si denote the vote/seat shares of then competing parties.11 Using the continuous measure of effective threshold to predict disproportionality scores for the

seventy elections (in seventeen countries) in a simple bivariate regression model yields the followingresults (standard errors in parentheses; adjustedR2 5 0.70): least squares index5 1.6 (0.5)1 0.32(0.025)*Teff. The empirical robustness of this relationship is suggested by the fact that Lijphart witha somewhat different set of countries, elections and equation specification, reports a very similarcoefficient of 0.32 for the influence of effective threshold on disproportionality (Lijphart,ElectoralSystems, p. 108.)

12 Several comments on the graph are in order. First, the exact slope of the regression line naturallydepends on the (somewhat arbitrary) choice of an effective threshold value for the SMD systems.Secondly, there are several noticeable outliers in the medium range of effective threshold. These casesare the pre-1989 Norwegian elections, as well as the five Spanish cases. Both of these systems feature


Fig. 1. Disproportionality by effective thresholdNote: SMD systems are assigned an effective threshold of 35 per cent.

A BASELINE MODEL OF NA ÏVE VOTERS AND PARTIES

In order to set up the remainder of our argument, in which we move beyonddisproportionality as a measure of the quality of representation, let us begin witha very intuitive, if constrained, approach to understanding how election rulescan shape the translation of the distribution of citizen preferences into thedistribution of legislative party positions. First, let us assume that thedistribution of citizen preferences is reasonably approximated by a normal,bell-shaped curve. In fact, for the countries that we shall be examining this isempirically a well-founded assumption in the 1980s and 1990s. Table 1 showsthe distribution of citizen self-placement on the left–right scale for our seventeencountries in the early 1980s. Examination of the citizen distributions in the early1990s shows no striking differences.

To explore the implications of different election laws, let us assume initiallythat there are ten parties, each offering election promises corresponding to theten positions on the left–right scale. Let us also assume, in this ‘nai¨ve’ baseline


higher thresholds, but also suffer from substantial malapportionment of seats across districts. Wecannot disentangle the effects here, but this malapportionment undoubtedly leads to someover-attribution of disproportionality. Note that disproportionality in Norway declined from about6 to about 4 after the rules were revised, decreasing effective magnitude as well as improvingapportionment (see appendices on the internet version of this article) Thirdly, we classify Australiaand France with the other (simple plurality) single-member district systems (as does Lijphart), despitespecial features of their election rules (preferential vote, two-round majority vote). While thesespecial features may well affect party competition, their impact on difficulty of entry to the legislature,and especially the local–national cancellation problem discussed below, is similar to the simpleplurality systems.

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TABLE 1 Voter Self-Placement on Left–Right Scale: Early 1980s or Closest Election Survey

Citizens (%) at Each Scale Point†

Country Year 1 2 3 4 5 6 7 8 9 10 Med. Mean SD

Australia 1981 2 1 6 9 36 14 12 10 4 5 5.5 5.8 1.9Austria 1975 3 3 10 10 16 19 13 14 6 7 6.0 6.0 naBelgium 1981 3 4 9 8 21 22 11 9 4 9 5.7 5.8 2.2Canada 1981 2 1 4 6 37 20 12 11 4 4 5.7 5.9 1.8Denmark 1981 3 3 7 10 31 17 13 9 5 3 5.5 5.6 1.9Finland 1981 2 3 7 11 26 14 13 15 6 3 5.7 5.9 2.0France 1981 7 5 15 13 31 11 9 5 1 3 4.8 4.8 2.0W. Germany 1983 1 3 10 15 28 14 14 9 4 3 5.4 5.5 1.9Italy 1983 6 8 16 14 29 13 5 4 2 3 4.6 4.6 2.1Netherl. 1982 4 5 12 13 19 12 12 12 4 6 5.4 5.5 2.4N. Zealand 1981* 2 24 49 22 2 5.5 5.5 naNorway 1981 2 2 9 10 27 13 14 13 4 6 5.7 5.8 2.1Spain 1981 4 7 16 16 25 13 9 7 2 2 4.8 4.9 2.0Sweden 1981 3 6 14 12 22 12 11 11 5 5 5.3 5.4 2.3Switzerl. 1976 2 1 9 11 25 18 13 12 4 4 5.7 5.8 naUK 1983 3 2 7 10 27 16 14 14 4 4 5.7 5.8 2.0USA 1981 2 4 6 7 26 18 14 12 5 6 5.8 5.9 2.1

* The survey in New Zealand (Clive Beanet al., New Zealand Voting Survey, Post Election 1981(Canberra: SocialScience Data Archives, 1981)) used 1–5 scale; however, mean and median were recomputed as if based on a ten-pointscale.†Most 1981 distributions and scores are from the 1981 World Values Study. Others in the early 1980s, but not 1981,are from closest Eurobarometer surveys. Mid-1970s scores in Austria and Switzerland from the Barnes and Kaaseeight-nation study, as these are not included in the 1981 World Values Study. However, they are included in the 1990World Values study and subsequent analysis uses those data.


model, that each voter votes for the party closest to him or her. Initially, considerthat the election rules provide for a single national, multi-member district inwhich all parties gaining over 0.67 per cent of the votes win a percentage oflegislative seats proportional to their percentage of the vote. (This characteriza-tion corresponds roughly to the electoral rules used in the Netherlands.) Giventhese circumstances we can see that the election outcome would result in all tenparties attaining legislative representation and a distribution of preferences inthe legislature extremely similar to the distribution of preferences in theelectorate. Specifically, there would be: (1) no vote–seat disproportionality; (2)a close match between the standard deviations of citizen and legislativepreference distributions; (3) close correspondence between the citizen andlegislative medians.

Now, we can consider what would happen if we gradually increased theminimum percentage of the votes necessary to qualify for seats in the legislaturewhile holding constant the number of parties and the assumption of sincerelyvoting citizens. Obviously, as we increase the threshold, parties at left–rightpositions favoured by small numbers of citizens start to drop out. We can seethat with the citizen distributions in Table 1, as we approach about 5 per cent,a number of small parties would be disqualified in each country. As we approach10 per cent, more parties would be eliminated. Given the ‘bell-shaped’distributions seen in Table 1, these would continue almost everywhere to beparties at the two extremes. While Table 1 suggests some asymmetrical‘lumpiness’ at a few points, the effects are pretty smooth, and they continue, eversharper as we approach even 20 per cent.

This baseline model suggests that as we increase the threshold, we wouldobserve: (1) increasing vote–seat disproportionality, as small parties areeliminated; (2) declining variance in the preferences in the legislature, bothabsolutely and relative to the citizen variance, because the eliminated partiestend to be those at the extremes;13 (3) continued good approximation betweenthe median ideological position in the legislature and the median ideologicalposition of the electorate. Moreover, as the threshold increases, at some pointthe median party in the legislature will gain a majority of seats. This majoritywill be associated with relatively high vote–seat disproportionality and, at thesame time, with good correspondence between the citizen and legislativemedians. These results would presumably please majoritarian theorists, but bedisturbing for those who favour broader representation of all points of view inpolicy negotiations. It is precisely this expected pattern of high disproportion-ality, reduced variance and good correspondence of medians that should makeus wary of assuming that disproportionality in vote–seat relationships willnecessarily be normatively undesirable for everyone. High disproportionalitycan coexist with good representation as measured by other criteria, e.g. mediancorrespondence.

13 We shall not explore the question of the relationship between the variances of citizen andlegislative preferences in this article, but it remains an interesting subject for further analysis.


The imagined results of our base-line model are, on the surface, implausible.They assume that politicians and voters will ignore the increase in the thresholdas they form and support parties, and as the parties choose policy positions. Onthe contrary, strategic politicians and strategic voters should prefer not to wastetheir efforts/votes on policy positions/parties that are likely to lose. In the nextsection we reconsider the implications of increasing the threshold if we allowfor such strategic behaviour.

ELECTION RULES AND VOTE–SEAT DISPROPORTIONALITY

The base-line model provides us with certain expectations about the manner inwhich rising thresholds are going to affect the relationship between votes andseats. However, there are several difficulties with this naı¨ve view of the waythresholds work. One difficulty is that it is highly implausible that voters and,especially, politicians will be so naı¨ve as to ignore the effects of higherthresholds as they cast votes and organize political parties. A second difficultyrelates to the manner in which we conceive of disproportionality in the firstplace. Parties gain votes and seats at the district level, but disproportionalityscores are calculated at the national level. These complications can introducesystematic downward pressures on vote–seat distortion in high thresholdsystems.

Downward pressures on disproportionality in high threshold systems

In the base-line model, we assumed that voters and politicians do not actstrategically. Sophisticated voters and politicians should anticipate the effectsof electoral systems and respond. Such strategic behaviour is likely to affectwhom voters support, which parties will be sustained by politicians, and wherethese parties will locate in ideological space. A large body of theory hasaddressed this problem. Gary Cox provides the most recent and extensivetreatment, which explicitly extends and integrates the work of those in theDuverger tradition with results in positive political theory.14 Cox generalizesDuverger’s famous ‘law’ that single-member district rules tend to propeltwo-party systems into what he calls the ‘M 1 1 rule’. According to this rule,the number of parties in equilibrium will be no greater thanM 1 1, whereM isthe district magnitude. The intuitive reason for this result is that if more thanM 1 1 parties exist, some of them are certain not to gain representation, andstrategic voters will desert them in favour of parties that may gain entry into thelegislature. In response, strategic politicians will not form more thanM 1 1parties. A slightly different terminology says that the ‘carrying capacity’ forpolitical parties of an electoral system is defined byM 1 1. Under Cox’sM 1 1rule, we would therefore expectfewerparties to compete in higher threshold

14 Gary Cox,Making Votes Count: Strategic Co-ordination in the World’s Electoral Systems(Cambridge: Cambridge University Press, 1997).


systems. Because a reduction in the number of parties limits the number ofparties that can be excluded (in the limit to one party), it can also reduce thepotential for vote–seat distortion. As a consequence, disproportionality mayincrease less with increases in the effective threshold than our base-line modelmight lead us to expect. This first type of downward pressure is essentially thephenomenon discussed by Taagepera and Shugart as the ‘Law of Conservationof Deviation from Proportionality’.15

A second complexity has received less attention. This complexity is createdby the particular understanding of disproportionality prevalent in the literatureon electoral law. Disproportionality is usually thought of as a national-levelproblem and disproportionality scores are calculated using national-level voteand seat shares. However, parties gain votes and seats at thedistrict level. Insome electoral systems, these two levels coincide (for example, the Nether-lands). In most circumstances, however, a nation’s geographic area issubdivided into a number of electoral districts. Such subdivision opens up thepossibility that over and under-representation for individual parties cancels outover the various districts. The final disproportionality score will thereforedepend on the manner in which seat and vote shares across electoral districtsadd up and cancel out as we calculate national vote and seat shares.

A simple example can illustrate this. Assume an SMD plurality rule systemwith two districts of equal size. In the first election, partyA wins 49 per centof the vote in District 1, and 49 per cent of the vote in District 2, while partyB captures the remaining 51 per cent in both districts. PartyB’s national voteshare is 51 per cent and its seat share is 100 per cent. The disproportionalityindex is equal to 49. In the second election, partyA wins 49 per cent in District1, and 51 per cent in District 2, whileB wins the remaining votes.B’s nationalvote share is 50 per cent, its vote share is 50 per cent, and the disproportionalityindex is equal to zero. The huge shift in the index in response to a mere 1 percent shift in the national vote share is created simply by a change in the mannerin which over- and under-representation do or do not cancel out over districtsas we aggregate to the national level. ‘Cancellation’ effects can play animportant role in determining vote–seat disproportionality.

These cancellation effects are likely to be particularly important in SMDsystems, and of less significance in PR systems. PR systems typically employa relatively small number of electoral districts with high magnitude to elect theirparliaments. Moreover, the allocation rules are designed to reflect vote and seatshares fairly accurately. As a result, the percentage of the vote that can be‘wasted’ by any one party in a given electoral district is constrained to berelatively small. When we aggregate across electoral districts to the nationallevel, we are therefore aggregating over a limited number of units, each of whichdoes not experience high vote–seat distortion. Even without ‘cancelling’ effectsacross districts, we therefore do not expect to see much disproportionality at the

15 Taagepera and Shugart,Seats and Votes, p. 123; Cox,Making Votes Count, p. 173.


national level.16 Of course, this is exactly what these systems aim at. The pointof PR systems is precisely to reflect the vote distribution as closely as possibleinto the legislative distribution, and their success in doing so is evident inFigure 1.

In SMD plurality rule systems, however, the percentage of the vote that canbe ‘wasted’ in any given district can be, and usually is, quite substantial,especially if the race is competitive. In aggregating to the national level, we areaggregating over a large number of districts, each of which is likely toexperience high disproportionality. The disproportionality at the national levelwill therefore depend crucially on the ‘cancellation effects’ across electoraldistricts, i.e., on the manner in which parties are ‘compensated’ for under-representation in some districts by over-representation in others.17 Ifcancellation works well, disproportionality can be low in SMD systems eventhough there is large distortion in each individual district. If cancellation fails,however, disproportionality can be substantial. The precise point of partisangerrymandering in SMD systems is to exploit this fact by ensuring that thecancellation process (or rather, the failure thereof) systematically works againsta particular party.

Failures to reduce disproportionality: co-ordination and convergence failures

These downward pressures create the potential for high threshold systems tofeature low disproportionality. However, it is unlikely that they will systemat-ically depress vote–seat distortion to the level prevalent in low thresholdsystems. This is so because a number of conditions must be met in order to makethe downward pressure of high threshold systems effective. First, the numberof parties must be reduced in order to limit the potential for wasted votes.Secondly, wins and losses must cancel in significant ways across districts. Thedisproportionality of such systems is therefore highly susceptible to any failureof these conditions to be met.

Consider the difficulties introduced by the cancellation process. Higherthresholds create the potential for higher disproportionality at the district level.Whether or not this disproportionality will carry over from the district-level tothe national-level will depend on cancellation, i.e. on how under- andover-representation for parties will cancel across districts. Since the deviationsthat must be balanced are potentially larger the higher the threshold, cancellationeffects will take on greater significance in high threshold systems. As a

16 This argument implicitly assumes that the number of parties does not exceed the carryingcapacity of the electoral system in significant ways. If there are ‘too many’ parties competing, andmany fail to gain representation (for example, by falling below a legal threshold), disproportionalitycan be very high even in PR systems. The Russian parliamentary election of 1995 provides a perfectexample. Of the twenty-seven parties competing, twenty-three fell below the 5 per cent threshold,making them ineligible for distribution of list seats. The least squares index for the election is equalto 11.1, rather large by any PR standards.

17 See also Taagepera and Shugart,Seats and Votes, pp. 109–10.


consequence, higher threshold systems will be more susceptible to cancellationfailures, and such failures impose greater costs in terms of disproportionality.In particular, we do not expect cancellation to work efficiently when systematicdistortions favour one or the other party in the races, leading one partyconsistently to finish in second (or third, etc.) place. A number of events canproduce such distortions. The most significant and obvious one would be afailure of one, or both, of the parties to converge to the median voter. If votersare systematically favouring one party, it is unlikely that the over-representationof the favoured party will be balanced out by losses in other districts. Short-termeffects, such as scandals, economic performance, or the popularity of aparticular political figure may also lead to distortions that hinder effectivecancellation.

Moreover, a failure to reduce the number of parties is likely to exacerbate thiscancellation problem.18 The larger the vote share that can be wasted by a partythat does not gain seats or that is severely under-represented in the legislature,the higher vote–seat distortion will be. Clearly, this cost of a failure to reducethe number of parties increases with the threshold. Since in SMD systems,multi-party competition usually implies that some parties are severelyunder-represented in the legislature, failing to co-ordinate on the proper numberof parties is particularly disastrous for disproportionality in SMD systems.19 Atthe same time, these systems are the most likely to feel the constraint of theM 1 1 rule because their carrying capacity for political parties is low. (Theeffective numbers of parties in the PR systems in our dataset are almost certainlyall below the carrying capacity of those systems.) SMD systems are thereforeespecially susceptible to this co-ordination failure. Indeed, there is someprimafaciaevidence that failure to reduce the number of parties in SMD systems doesincrease disproportionality. For the twenty-one SMD elections in the set, thesimple Pearson correlation between the effective number of parties in theelection and the disproportionality score is 0.48, (significant at the 5 per centlevel assuming the appropriateness of ordinary regression).20

The most important implication of our argument is that SMD systems do not

18 As Cox (Making Votes Count, pp. 79f.) points out, the reduction toM 1 1 parties poses aco-ordination problem faced by politicians and voters. Voters have an interest in concentrating theirvotes on parties that can gain representation. Politicians, in turn, want to co-ordinate by only offeringparties that can gain sufficient support, and refrain from maintaining permanent losers. Creatingmutual expectations about theparticular parties that will gain sufficient votes is the co-ordinationproblem that must be solved. If this problem is not solved, too many parties will be competing withthe result that several parties are shut out of the legislature. Several things can account for such failureto reduce the number of parties. There may be insufficient information to create clear expectationsabout which parties will not gain representation and should therefore withdraw. Or politicians maycare intensely about the future, and stay in a race not to win, but to establish a position for comingelections. In either case, we would not expect parties to disappear in response to strategic behaviour.

19 The 1983 election in Britain provides a particularly powerful example of this. TheSocial-Democratic/Liberal Alliance gathered 25.4 per cent of the national vote, but only ended upwith 3.5 per cent of the seats precisely because they ended up in second place in many constituencies.

20 Also, see the data displayed in Figure 10.1 of Taagepera and Shugart,Seats and Votes, p. 107.


necessarily lead to high disproportionality, but merely have the potential forsuch distortion, depending on how effectively the downward pressures we havediscussed – strategic reduction of parties and cancellation effects – serve toreduce disproportionality. These downward pressures are dependent on anumber of contingencies. The importance of these contingencies (which mayor may not hold in any particular election) suggests that disproportionality inSMD systems should vary to a greater extent than disproportionality in PRsystems. This conclusion produces a testable prediction. If we are right, thestandard deviation of disproportionality should be much larger in SMD systemsthan in PR systems. The scatter plot in Figure 1 suggested such a pattern. Table2 (on p. 401), which shows the means and standard deviation of disproportion-ality across four categories of the effective threshold, confirms that this is thecase. The standard deviation of disproportionality in the SMD systems isstrikingly higher than in any of the three categories of PR systems. It is a littlemore than double the standard deviation of all PR systems combined. Clearly,disproportionality varies to a much greater extent under plurality rule.

ELECTION RULES AND CORRESPONDENCE OF MEDIANS

Increasing the effective threshold of an electoral system thus clearly leads, onaverage, to higher disproportionality and greater variation in disproportionality.This is one main reason why some theorists have concluded that PR systemsdeliver better representation than Westminster, SMD systems. However, in ournaı̈ve baseline model (assuming multiple parties and sincere voters), wesuggested that poor representation in the sense of vote–seat disproportionalityneed not imply poor correspondence of the citizen and legislative medians.Increasing the effective threshold implied increasingly poor vote–seat corre-spondence, but relatively unchanging correspondence between the position ofthe median voter and the median legislator. In this section we want to find outwhether electoral rules do in fact make little difference for correspondence ofthe preference medians. As far as we know, this has not previously beeninvestigated. Should the implications of the naı¨ve model fail to hold, we wantto try to understand why they do not. For the question of median correspondence,the number of political parties is less important than the positions they take inideological space relative to voters. We thus begin by asking about thesubstantive party positions various electoral systems are likely to generate.

Theoretical Foundations of Median Correspondence under PR

There is relatively little rigorous analysis of the incentives created by PR rulesfor ideological party competition.21 Such theoretical results as we do have tendto support the intuitive notion, broadly confirmed by empirical evidence,

21 David Austen-Smith and Jeffrey Banks, ‘Elections, Coalitions and Legislative Outcomes’,American Political Science Review, 82 (1988), 405–22; Gary Cox, ‘Centripetal and Centrifugal


that PR systems (provided there are more than two parties competing) encourageparties to distribute themselves across the ideological spectrum. Cox has shownthat in equilibrium, parties should position themselves along the left–rightdimension at intervals roughly equal in terms of the percentage of the electoratelocated between them.22 Austen-Smith and Banks, assuming that voters actstrategically, derive a similar result, with one party taking the position of themedian voter while the other two parties in their model locate symmetricallyaround the median. As Cox has concluded, ‘equilibria in multi-party PR systemsare expected to be such that (1) each party has a fairly well-defined and narrowideological appeal, and (2) parties are dispersed fairly widely over theideological spectrum.’23

A pleasant consequence of these results is that PR systems in general holdout great potential for good median correspondence. The position of the medianvoter should be closely represented by a party. At worst, if there is an evennumber of evenly-spaced parties, the two most centrist ones will be equidistantfrom the median.24 And if the voter-distribution is dense so that most voters areclustered around the median (as in many of the empirical distributions in Table1), the two closest parties should not be very far away from the citizen median.If a very high threshold, historical or cultural circumstances, or economies ofscale reduce the number of parties competing in a PR system to only two, thena single party will achieve a majority and, by definition, will include the medianlegislator. Good preference correspondence will then depend entirely on thewinning party being at the position of the median voter. Fortunately forcorrespondence (and normative majoritarian theories of desirable representa-tion), Downs’s theory of two-party competition predicts convergence of bothparties to the position of the median voter.25 Under any national PR system,regardless of threshold, we can therefore expect good correspondence of citizenand legislative medians and (in that sense) good preference representation. Wecan also predict fairly clearly the circumstances under which good preferencerepresentation would fail:

(1) If the number of parties is not reduced as the threshold increases, or if partiesfail to find the proper competitive spaces, substantial distance between thecitizen and legislative medians can result. In particular, if too many partiescompete for the same ideological position, they might split the vote around


Incentives under Alternative Voting Institutions’,American Journal of Political Science, 34 (1990),903–35.

22 Cox, Making Votes Count, p. 230.23 Cox, ‘Centripetal and Centrifugal Incentives under Alternative Voting Institutions’, p. 922.24 Cox (Making Votes Count, p. 230) suggests an upper bound of (1/(M 1 1)) as the largest niche

that can exist between two competing parties under PR. This implies that distance from the medianshould be bounded above by (1/(M 1 1)/2) of the citizenry. Given the centrist distributions of oursample, which tend to have 25 per cent of the citizenry clustered around the median, this should bequite close.

25 Anthony Downs,An Economic Theory of Democracy(New York: Harper and Row, 1957).


that position in such a way that a substantial number fall under the threshold.As a result, the position will not be appropriately represented in thelegislature. If this happens, the legislative median will shift. Depending onthe exact location of the voter median, this may increase the distancebetween citizen and legislative median. (Note that this form of failurealways implies vote–seat misrepresentation, but it only contributes topreference misrepresentation under some circumstances.)

(2) If no party or parties locate in the region of the citizen median, or if votersfail to support the ones that do, naturally the legislative median must emergeat some distance from the citizen median. Similarly, in a two-party situation,if both parties fail to converge to the median voter, or if the party locatedat the median does not win a majority, the winner will have the legislativemajority position and be off the median.

Theoretical Foundations of Median Correspondence in SMD Systems

Correspondence between medians in single-member district systems presentsgreater theoretical complications. On the one hand, the pure theory of electoralcompetition in these types of systems predicts that they should experiencetwo-party competition for the position of the median voter.26 Accordingly,correspondence between medians should be good. However, this predictiondepends on a number of specific conditions that are usually left undiscussed,namely: (a) the number of parties, (b) the constraints placed on districtcompetition by national party labels and organizations, (c) the relationshipbetween the median voters in the districts and the median voter nationally.27 Itis noteworthy that this ‘district–national’ problem, which we already encoun-tered in the ‘cancellation problem’ for disproportionality, re-emerges here.

These conditions are important because parties face problems in determininghow much to adapt their national positions to the local preferences and whereto compete when district medians vary substantially across districts. Parties mayhandle this in different ways depending on the organizational and institutionalfeatures that shape cohesion of party promises and behaviour.28 They may

26 Cox,Making Votes Count; Downs,An Economic Theory, Maurice Duverger,Political Parties:Their Organization and Activity in the Modern State, translated by B. North and R. North (New York:John Wiley, 1954).

27 Downs’s and Cox’s theories are both district-level theories that avoid the ‘local–national’problem (especially points (b) and (c)) by sticking to district-level competition. The problem emergeswhen we generalize from the district-level to the national level. One situation is fairly simple. If thereare only two parties, and the geographic districts have roughly the same median preferences as thecountry at large, then each district should have Downsian convergence to the median by both parties.The parties face no ‘local–national’ problem in seeking the median. It will not matter which partywins in a given district, or which wins more districts. The legislative winner, who holds the medianlegislator, will be at the voter median. This, in essence, is the situation usually assumed when wegeneralize from Downs’s and Cox’s district-level theories to the national level.

28 Fiona McGillivray, ‘Comparative Institutions and Policy Outcomes’ (unpublished doctoraldissertation, University of Rochester, New York, 1994).


choose to run a national campaign and not adapt to local conditions, or they mayrun localized campaigns and worry less about a consistent national image.Nevertheless, even if cohesive two-party competition at the national level wereto result in at least one party offering the policy-position of the median (national)voter, a legislature may result whose median sharply diverges from the citizenmedian. Similarly, even if parties adapt to local conditions and converge to theposition of the median voter in the districts, a legislature can emerge whosemedian is located far away from the national citizen median.29 Moreover,variation in district medians is not uncommon. It can be created by geographicvariations in preferences (such as in Canada), but also by malapportionment(districts containing different numbers of constituents), or by gerrymandering(drawing district boundaries to partisan advantage.) Indeed, this would seemprecisely to be the point of much gerrymandering. The effects of thisdistrict–national problem on the correspondence between national citizen andlegislative medians are fairly unpredictable.

A second complication is connected to the number of competing parties. Ifmore than two parties compete in a district under single-member districts, theresults are unpredictable. The current state of research suggests that thereprobably are no equilibria configurations for party placement under pluralityrule in one dimension if more than two parties are competing. However, if anysuch equilibrium does exist, the competing parties must be somewhat dispersedacross the ideological spectrum.30 The parties need not converge to the districtor national medians to maximize their chance of winning. The legislativemedian may well reflect this non-convergence, especially if the parties arenationally cohesive. Thus, the clearest predictions for single-member districtsare:

(1) Preference representation may fail in purely two-party systems if the pureDownsian model fails – if the role of activists, multiple levels of candidateselection (primaries and general elections) or a concern about variation inthe geographic configuration of preferences within and across districts leadtwo dominating parties to fail to converge to the national median.Obviously, these considerations do not mean the parties are not actingstrategically, just that additional factors are potentially relevant to theirstrategic decisions. It is noteworthy that, here, as in the analysis ofdisproportionality, SMD systems are distinct in that they raise additionalconsiderations because of the geographic distribution of preferences.

(2) Preference representation may well fail if more than two parties arecompeting against each other in the districts. This can be a co-ordinationproblem in Cox’s sense.31 Multiparty competition may then lead strategi-cally acting parties to fail to converge to the median voter, with all the

29 See the appendices to the internet version of this article for analytic examples.30 Cox, ‘Centripetal and Centrifugal Incentives under Alternative Voting Institutions,’ p. 913f.31 It should be noted that Cox (Making Votes Count, p. 75) delineates some conditions under which

multi-party competition can constitute ‘Non-Duvergerian’ equilibria.


geographic considerations also operating to create variance in theexpectations. Moreover, the presence of multiple parties may split the votesin a way such that the party closest to the median is not even the pluralitywinner. This is a special version ofM 1 1 failure, but one with potentiallyvery large impact on preference correspondence.

Empirical Tests of Election Rules and Preference Misrepresentation

To test preference (mis)representation we need direct measures of thepreferences of citizens and of the positions of the parties in the legislatures.32

Naturally, it is conceptually and empirically difficult to measure the relationshipbetween citizens’ preferences and parties’ positions and policies in differentcountries. Public policy in modern society covers an enormous range of possibleactivities. Different societies have different needs and different traditions. Evenwithin the same countries different citizens care about different issues.Moreover, many citizens will be uninformed about the details of policy issuesand the reasonableness of different alternatives. A common response in the faceof this complexity consists in collapsing the problem of identifying a citizen’sdetailed policy preferences into a stance towards a general policy direction inthe discourse of the citizen’s society.

The instrument that we use for doing so here consists of a voter’sself-placement on the ‘left–right’ ideological continuum, obtained from variousEurobarometer surveys and the two World Values Studies. In the democraciesin our analysis in this period, the language of ‘left’ and ‘right’ reflects a (loosely)unidimensional discourse familiar to citizens and elites. It is not only the mostwidely available single measure of the preferences of citizens in differentcountries, but seems to meet better than any alternative our need to capturecomparably the general stances of citizens and the general policy orientationsof the parties that compete for policy-making positions. Over the years, theleft–right language has assimilated various specific issues and alternatives thathave become important to voters and the parties who appeal to them. In the1960s and 1970s the degree of government ownership in the economy wasperhaps the most important component, although views on defence policy alsomattered. The former issue was revitalized by debate about denationalizationin the 1980s, while the collapse of international communism made relations withthe Soviet Union less important. In some countries ‘left and right’ encompassedviews on the role of the Church in politics, in others it did not. With the rise of‘new politics’ issues of environmental protection and citizen participation, theleft–right dialogue also came to incorporate these issues to varying degrees in

32 We assume that ‘party’ is the appropriate unit in the legislature, given the very highly cohesiveparty voting in the legislatures of virtually all these (parliamentary) systems (see Michael Laver andNorman Schofield,Multiparty Government(Oxford: Oxford University Press, 1990) Appendix A).The legislative median is the position of the party that contains the median legislator, assuming allmembers of the party take the same position.


different countries.33 In the United States, the terms ‘liberal’ and ‘conservative’are used with similar meaning in this discourse. Although the degree to whicha single dimension successfully assimilates the different issues no doubt variesacross party systems, the left–right scale seems fairly effective in assimilatingmany different issues and reducing them to a single dimension. Studies of masspublics and political elites in many of our countries show that they are able tothink about public-policy issues using the language of left and right and to placethemselves meaningfully on this scale.34

We employ a ten-point left–right scale in the analysis that follows. It is criticalto emphasize that we do not assume that the same numerical position on thisscale implies the same substantive policy position in different countries. Almostcertainly, it does not. A middle of the road position on health policy in the UnitedStates is quite different than a centrist position on health policy in Britain.However, as long as the distances between points are roughly comparable acrosscountries, this divergence in substantive positions is irrelevant. After all, we donot want to compare the preferences of citizens in one country to the preferencesof citizens in another country, but only the divergence between citizen and partyposition in the legislature within one country. To place parties on the left–rightscale, we are fortunate to have available two surveys that asked country expertsto place the parties in their countries on a ten- or eleven-point left–right scale.35

These surveys are of great value because they do not focus on internationalstandards of left and right, but should tap the national political discourse, andthus be comparable to the self-placement of the citizens of the specific country.36

33 Inglehart, ‘The Changing Structure of Political Cleavages’, pp. 25–69.34 See especially Inglehart and Klingemann, ‘Party Identification, Ideological Preference, and the

Left–Right Dimension among Western Mass Publics’. Also see Samuel H. Barnes,Representationin Italy: Institutionalized Tradition and Electoral Choice(Chicago: University of Chicago Press,1977); Francis Castles and Peter Mair, ‘Left–Right Political Scales: Some Expert Judgments’,European Journal of Political Research, 29 (1984), 73–88; Philip E. Converse and Roy Pierce,Political Representation in France(Cambridge, Mass.: Harvard University Press, 1986); RussellDalton, ‘Political Parties and Political Representation: Party Supporters and Party Elites in NineNations’,Comparative Political Studies, 18 (1985), 267–99; Russell Daltonet al., eds,ElectoralChange in Advanced Industrial Societies; Huber, ‘Values and Partisanship in Left–RightOrientations’; John D. Huber and Ronald Inglehart, ‘Expert Interpretations of Party Space and PartyLocations in 42 Societies’,Party Politics, 1 (1995), 73–111; Ronald Inglehart,Culture Shift inAdvanced Industrial Society(Princeton, NJ: Princeton University Press, 1990). However, we mustbe cautious about using this tool in new democracies where the left–right (or other) language ofdiscourse may not have had time to settle on common meanings. Survey and anecdotal evidencesuggest that in Russia in the early and mid-1990s, for example, there was considerable disagreementabout the meaning of ‘left’ and ‘right’ as descriptions of positions on the critical issue of transformingof the old command control economy. See the discussion and analysis of the substance of left andright positions in different countries in Huber and Inglehart.

35 Castles and Mair, ‘Left–Right Political Scales’; and Huber and Inglehart, ‘Expert Interpreta-tions of Party Space and Party Locations in 42 Societies’. We reconfigured the eleven-point scaleemployed by Castles and Mair to obtain placements on the ten-point scale (see appendices on theinternet version of this article).

36 In a relatively small number of surveys, principally those associated with the EuropeanElections of 1989 and 1994 (but also in Australia 1996, New Zealand 1993 and in Sweden generally),


TABLE 2 Vote–Seat Disproportionality and Distance between Citizenand Legislative Medians by Type of Election Laws

Distance oflegislative (party)

median fromDisproportionality citizen median†

NStandard Standard of

Election law category Mean deviation Mean deviation cases

PR effective thresholdBelow 4% 1.7 (0.53) 0.68 (0.51) 204% to 7% 2.7 (1.04) 0.49 (0.45) 207.1 to 13% 7.1 (1.97) 0.94 (0.94) 9

Single Member Districts 12.5 (5.02) 1.47 (0.71) 21Totals 5.9 (5.47) 0.89 (0.74) 70

*Gallagher disproportionality index; see fn. 10.†Party positions on left–right scale from Castles and Mair (transformed to ten-pointscale) and Huber and Inglehart; citizen positions primarily from World Value andEurobarometer surveys; see appendices on the internet version of this article.

Table 2 shows the averages and standard deviations of vote–seat dispropor-tionality and the absolute distance between median citizen and the medianlegislative party position across four categories of effective threshold. The firstcolumn reaffirms the discussion above: higher effective thresholds areassociated with ever greater disproportionality of party representation in thelegislature. The second column shows that the standard deviation of dispropor-tionality also increases sharply with the effective threshold, as we predictedabove.

Table 2 also shows the absolute distance between the median citizen and thelegislative median. Here we see that the low and medium-low PR systems aresuccessful in electing legislatures whose median is quite close (about 0.6 of apoint on the ten-point scale) to the citizen median. The high threshold PR


citizens were asked to place the parties on a left – right scale. Despite some obvious individual errors,the mean citizen placements of the parties correspond closely to the expert placements in Huber andInglehart’s 1993 survey. Using eighty parties in thirteen countries (including Portugal and Ireland)the correlation between mean citizen placement of a party and the expert placement was 0.92; theunstandardized regression coefficient in an equation using the citizen placement to predict the expertplacement was 1.08 (intercept5 2 0.44). Most of the relative outliers are small parties. If we lookat the ten legislative median parties in the latest election used in our primary analysis and for whichboth data are available (excludes Austria, Canada, Finland, Italy, Norway, Switzerland, UnitedStates), the regression coefficient is 0.99 (intercept5 2 0.12),R2 5 0.91. Despite the small numberof cases, which prevents our using citizen estimates to replicate the general analysis, the closecorrespondence strongly supports the comparability of expert party placements to citizenself-placements in the local discourse.


systems show greater average distances and greater standard deviations.However, it is the SMD systems that stand out most strikingly as failing toachieve good correspondence between citizen and legislative medians. Theaverage legislative median is more than twice as far from the median citizen inthese systems as in the PR systems.

The results for the PR systems are, on average, consistent with our theoreticalexpectations. There is substantial variance (the standard deviation is about aslarge as the score itself in the PR systems), but most of these systems seem tobe performing rather well in creating correspondence between median citizenand median legislator. The results for the SMD systems, by contrast, are quitecontrary to the theoretical expectation. On average the median legislator isone-and-a-half scale points from the median citizen in these systems. Given thesharp divergence from theoretical expectations in the single-member districtsystems, but not (on average) in the other systems, the puzzle of this particularrepresentation failure is the target of further analysis below.

Before moving on to this task, however, it is useful to ‘cross-check’ our resultsby confirming the robustness of the distinct difference between the relativelygood performance of the PR systems in achieving correspondence betweencitizen and legislative medians and the poorer performance of the SMD systems.To do so, we employ three alternative measures to estimate the distance betweenmedian citizen and legislator. The first two measures draw on a study that askedcountry experts to place the parties in their respective countries on severalspecific issue scales rather than on a general left–right scale.37 The Laver andHunt survey employed a twenty-point scale (which we converted to a ten-pointscale), and it was conducted roughly at the midpoint between our two mainexpert studies. Given the time period for our sample, the two issues includedin the Laver and Hunt analysis that seem to correspond most closely to thegeneral left–right scale consist of the items placing parties on the issues of publicversus private ownership in the economy and on the trade-off between taxes andservices.38 For each of these issues, we calculated the distance between themedian citizen position on the left–right scale and the median party position(where the median party is the median party according to that scale).

The third (and very different) alternative measure we employ to estimate theplacement of parties is provided by a large project that studied and coded themanifestos of political parties from the end of the Second World War until theearly 1990s (in most of our countries).39 Although these data were collected for

37 Michael Laver and W. Ben Hunt,Policy and Party Competition(London: Routledge, 1992).38 Respondents were asked to locate the position of the party leaders on ‘Public ownership’:

Promote maximum public ownership of business and industry (1); Oppose all public ownership ofbusiness and industry (20). Similarly, on ‘Taxes versus public services’: Promote raising taxes toincrease public services (1); Promote cutting public services to cut taxes (20.)

39 Ian Budge, David Robertson and Derek Hearl, eds,Ideology, Strategy and Party Change:Spatial Analyses of Post-War Election Programmes in Nineteen Democracies(Cambridge:Cambridge University Press, 1987).


other purposes, Laver and Budge developed a scheme for classifying manifestosentences as being ‘left’ or ‘right’ and determining the relative proportion of leftand right mentions to estimate the positions of the parties (naturally, the scaleruns from2 100 to1 100).40 Once again, we can use this measure to estimatewhich party contains the median legislator. However, it is still necessary totransform the proportion of mentions to correspond to the ten-point left–rightscale used by citizens. To do so, we use a standard ordinary least squares (OLS)regression to predict the expert placement position of parties in the Castles andMair and the Huber and Inglehart studies from the manifesto score and countrydummy variables, using all the parties for which we have data (a total of 260).The coefficients from this regression were then used to estimate a predictedten-point left–right position for each of the median parties according to themanifestos data.41 Once again, we can then calculate the absolute distancebetween the median legislator and the median citizen on the ten-point scale.

Table 3 shows the results of analysing this distance using the three alternativemeasures. The table reports results of a standard OLS regression in which theabsolute distance between median citizen and legislator is predicted using threedummy variables that correspond to the three PR categories. The SMD systemsthus comprise the missing category. Each column in the table corresponds toa different procedure used to measure the placement of the parties.42If the poorerperformance of the SMD systems is robust to the procedure used to measure theparty positions, then we should see consistently negative coefficients in all thecolumns and the coefficients should be of similar size, as all measures have beentransformed to the ten-point left–right scale. However, because the number ofcases varies and because the use of specific issues and of the manifestospresumably takes less account of the local context than the local experts on theparty systems would take, we expect fewer of the coefficients to be statisticallysignificant in the columns on the right of the table.

The table results are very reassuring for the robustness of the main results.On the far left we have replicated the results reported in Table 2 using thedummy-variable regression. This measure has the largest number of cases andis conceptually, we believe, the most appropriate general measure of mediancorrespondence. The negative coefficients of2 0.8 and 2 0.99 for the twolow-threshold PR elections show that the medians in those legislatures are

40 Michael Laver and Ian Budge, ‘Measuring Policy Distances and Modelling CoalitionFormation’, in M. J. Laver and Ian Budge, eds,Party Policy and Government Coalitions(New York:St Martin’s Press, 1992), pp. 15–40.

41 It is important to note that the manifesto classification scheme does not take account of the localpolitical discourse. Inspection of the manifestos’ data shows clearly that by the international codingcriteria, the discourse in some countries is more ‘left’ and the discourse in others more ‘right’. Hencethe need to add country dummies to the regression equation to calibrate the mid-point of the localdiscourse. We are grateful to Professor David Weimer for suggesting this approach.

42 Most procedures yield the same party at the median, but where they do not, the party that isthe legislative median on the scale in question is the one used to determine the distance from thecitizens. The samples on which the different regressions are based vary because not all measures wereavailable for all cases in the full dataset (see the appendices to the internet version of this article).

404P

OW

EL

LA

ND

VA

NB

ER

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TABLE 3 Election Laws and Left–Right Distance between Citizen and Legislative Medians: ByAlternative Measures of the Position of Median Party in Legislature

Regression coefficients (SE) using alternative party position measures

Expert issueplacement§ Party manifesto

proportionElection law Expert left-right Public Taxes v. left–rightcategory† placements‡ ownership services issue mentions¶

PR ThresholdBelow 4% 2 0.80 (0.20)** 2 0.80 (0.36)* 2 0.49 (0.34) 2 0.55 (0.21)**4–7% 2 0.99 (0.20)** 2 0.73 (0.37)* 2 0.35 (0.34) 2 0.56 (0.21)**7.1–13% 2 0.54 (0.25)* 2 0.60 (0.51) 2 0.38 (0.43) 2 0.10 (0.28)

Constant 1.47 (0.14)** 1.84 (0.26)** 1.36 (0.24)** 1.22 (0.15)**Number of cases 70 38 38 50R2 0.30 0.15 0.06 0.18

†Single Member District is reference category.‡Elections 1977 through 1987 use 1982 expert survey from Castles and Mair; eleven-point scale transformedto ten-point scale; elections 1988 through 1994 use 1993 expert survey from Huber and Inglehart.§Elections 1984 through 1994 use 1989 expert survey from Laver and Hunt; twenty-point scale transformedto ten-point scale.¶Elections 1977 through 1991 use Manifestos project data, with code left–right assignment from Laver andBudge; left–right proportions transformed to ten-point scale using regression of manifesto left–rightproportions and country dummies to predict expert left–right placement of all parties.*Significant at 0.05. **Significant at 0.01


nearly a full scale point closer to the citizen median than those produced by theSMD elections. At three-and-a-half to five times their standard errors thesedistances are highly significant (assuming the independence of the cases). Thehigh threshold PR cases are more similar to the SMD systems, but still asignificant distance closer to the citizen medians.

The next column of the table shows strikingly similar results using theLaver–Hunt measure of party positions on public ownership. All the coefficientsare also negative and even of roughly similar magnitude to those in Column 1.With many fewer cases (because the survey is only at a single time point) anda more specified issue, the standard errors are larger, but distances in the twolower threshold PR cases are still significantly less (at the 5 per cent level) thanin the SMD cases. Even the third column, which shows the tax/service trade-offissue, has consistently negative coefficients about the size of their standarderrors, although only 60 per cent the size of the coefficients in the first twocolumns. Finally, the last column shows the results based on the transformedmanifestos data. Once again, we see the familiar pattern of negative coefficients,with the two low threshold PR systems around half a scale point closer to thecitizen median than in the SMD systems. The standard errors are fairly low andthe differences from the SMD results are strongly significant. The highestthreshold PR systems, however, are only slightly closer to the median than theSMD systems. Nevertheless, these results also support the general pattern of thefindings.

We should re-emphasize that, in terms of conceptual fit, we are most confidentin the general expert left–right placements in measuring citizen–legislativedistances. It is also the case that these measures are the most widely availableand therefore maximize the observations on which the analysis is based. Thus,we view the three alternative measures primarily as secondary measures usedto validate the central result. Clearly, this cross-check confirms that the generalresult – on average the legislative medians are located at a greater distance fromthe citizen medians in the SMD systems than in the PR systems – is quite robust.It seems appropriate, then, to conclude by a more detailed examination of thesources of that distance, following our earlier theoretical expectations of wherethe connection might break down.

Party Competition and the Citizen Median in SMD Electoral Systems

Our expectations about good preference representation in the single-memberdistrict systems stemmed from the combination of predictions of two of the mostfamous theories of political parties: Duverger’s prediction that single-memberdistrict election rules will tend to be two-party systems and Downs’s theory thattwo-party competition will drive both parties to converge to the median voter.This combination is elegantly elaborated by Cox.43 We have already seen thatparties do not seem to reduce sufficiently in many of the single-member district

43 Cox, Making Votes Count, pp. 236f.

Canada80

France88

AUL93

AUL90US88

NZ81

US80Canada88

Canada79NZ90, 93

France93

France78

AUL83, 87France81

AUL80

UK87

UK92

UK79, 83

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Lose

r di

stan

ce fr

om m

edia

n ci

tizen

0.0 0.5 1.0 1.5 2.0 2.5 3.0Winner distance from median citizen


Fig. 2. Distance of parties from median citizen in single-member district elections

systems and this is associated with disproportionality in vote–seat representa-tion. Here we can begin by examining convergence to the median voter, theproximate ‘Downsian’ prediction. If this fails, we can consider why. Figure 2shows a scatterplot of the twenty-one single-member district elections in our set.The two dimensions show the left–right distance between the two largest partiesand the median voter. The horizontal dimension has the winning party and thevertical dimension shows the losing party. The Duverger–Downs predictionwould be that both parties should be close to the median voter, so that all thepoints should be located close to the point of origin.

Here, again, it is hard to know exactly what ‘close’ should be in the left–rightmetric, but we can recall that in the PR systems the median legislator was 0.64from the median citizen. It seems reasonable, then to assume that a fair‘Downsian’ prediction would be that both parties would be within or around thecrosshatched area of the figure. We would also predict the elections to be closeto the 45° line – parties are equi-distant from citizen median – and if they arenot, they should be above it (winning party is close to median). Of course, whatstands out overwhelmingly in Figure 2 is that none of the elections find the twolarge parties within the cross-hatched area. At least in comparison to the median


legislature in PR systems, the large parties in the SMD systems are just notvery close to the median voter.

If we look in more detail at Figure 2, we do see some elections that are closeto the 45° line, showing the winning and losing parties similarly distant fromthe median voter. The closest of these, in New Zealand 1981 and Australia1990, look a bit like the configuration discussed in our ‘naı¨ve’ high thresholdmodel. They have quite high disproportionality because of the elimination orserious under-representation of smallish parties. But because the main partiesare fairly close to the median, the correspondence of legislative and citizenmedians is fairly good – about one point away. New Zealand 1981 isespecially interesting from that point of view, because the winning Nationalparty actually received only 38.8 per cent of the vote and came in second invotes to the Labour party. With a non-plurality winner and very largedisproportionality (at 16.67, the fourth highest in our sample), the outcome isa representational disaster as measured by the vote–seat relationship. But interms of left–right distance from the electorate (0.9), the outcome is fairlyrespectable.

The United States is perhaps the best fit to the Duverger–Downs prediction,as that nation has the only truly two-party system among these cases and findsthe two parties fairly similar in distance from the electorate. But neither UScase matches Downs very well. In 1980 the Democrats (winning in thelegislature, but not in the presidential election, of course) are only about halfa point from the median, but the Republicans are nearly 1.5 points on the otherside of it. In 1988, the two parties are symmetrically distant from the votermedian – nearly on the 45° line – but each is about 1.4 scale points away. AsUS congressional studies have also shown, the parties diverged sharply fromeach other in the 1980s; they are about 2 scale points apart in the (recalibrated)Castles–Mair expert survey in 1982, but about 3 points apart in theHuber–Inglehart expert survey in 1993. No matter which side won under thelatter conditions, the legislative median would be more than double thedistance from the citizen median in the average PR system.

Moving out along the 45° line, we find elections with both partiesincreasingly far from the median. In the famous British election of 1983, bothmajor parties are very far indeed from the median voter, nearly 2.5 points,(although the winning party is slightly closer). As is, of course, empiricallywell known, this election is a disaster from the Duverger–Downs point ofview. There was very high disproportionality, with the Social Democratic–Liberal Alliance capturing about a quarter of the vote and only 3.5 per cent ofthe seats. With both traditional parties having diverged in opposite directions,no matter which main party had won the election, it would have been very farfrom the median voter. In France, too, we are not surprised to find the majoradversaries in 1978 and 1981, here represented by the closer individualparties, the Socialists and the Union pour la Democratie Franc¸aise (UDF),rather than the Socialist/Communist coalition versus the UDF/Gaullistcoalition – which would have been even further apart – far apart from each


other and the median voter. What is not so well known is the degree to whichelections in Australia at about the same time show a similar disaster for centrismand representation of the median voter.

There are quite a few cases of asymmetric convergence. That is, one partyis fairly close to the median, while the other is farther away. In strict two-partycompetition, we would, of course, expect the closer party to win. But in mostof these elections there are more than two parties competing and the variousways of splitting the vote lead to unpredictable outcomes. There is markedasymmetry (note the points well away from the 45° line) in all three Canadiancases, and in Britain, France and New Zealand in the later time period. In Canada1980, France 1988 and Australia 1993 the asymmetric competition was won bythe closer party. Despite large vote–seat disproportionality, these elections hadgood representation in the congruence of citizen legislative medians (andgovernments). Unfortunately for congruence in single-member districtsgenerally, however, such victories for the closer party were no more likely thanthe opposite.

In Canada the Conservatives ‘won’ in 1979 and again in 1988, showing upin Figure 2 with the ‘wrong party’ winner at a substantial distance from themedian. In 1979 this oddity is a result of the custom of allowing the largestlegislative party to form a minority government if no party wins a majority; thelegislative median was actually with the Liberals (and the Conservativegovernment soon collapsed, leading to a new election). In 1988 theConservatives won 57 per cent of the seats with only 43 per cent of the vote.Such under-representation of the two more ‘leftist’ parties appears as a classic‘co-ordination’ failure and leads to a legislative median far to the right of thecitizen median. In Britain in 1992 the winning incumbent Conservatives arefurther from the median than Labour, which is, however, still quite a way fromthe median. There is, in fact, a party near the median, the Liberal Democrats,who consistently lose the district races and fail to prevent single-party majoritiesin the legislature in the 1980s and 1990s. In New Zealand in 1993 the badly splitvote and high disproportionality again allowed the National party to win alegislative majority with under 40 per cent of the vote (actually only 35 per cent,although it was the plurality winner), but the party was nearly twice as far fromthe median voter as in 1981. The defeated Labour party had been repudiated byits left wing after its conversion to more conservative economic policies whilein office in the 1980s, and lost the 1990 and 1993 elections despite being closeto the citizen median. In France 1993 the defeat of the incumbent Socialists,which are much closer to the median, may testify to the power ofanti-incumbency vote apart from the left–right positionings.

We suggested in the theoretical discussion that the failure of the parties toconverge to the median would probably be the proximate cause of divergencebetween the citizen median and the legislative median in the single-memberdistrict systems. This is largely true. Most of the elections are multi-partycontests and Downsian convergence of both parties to the median is rare, at best.But there is more to the story. We also noted that in multi-party contests,


asymmetric competitions won by the ‘wrong party’ might feature importantly.The failure of the voters to support parties close to the national median, suchas the French Socialists and New Zealand Labour in 1993 and the British LiberalDemocrats generally, is indeed part of the picture in the single-member districtsystems. Generally, these outcomes can be explained by ‘co-ordination failures’in the sense that too many parties are competing. But they may also representdistrict medians that are rather different from the national median, some aspectof multi-dimensionality not consistently reduced to the single left–right scale(such as government scandals or foreign policy), inertia in citizen expectationsabout nationally ‘dominant’ and ‘minor’ parties, or something else.

It is clear that the Duverger–Downs–Cox predictions look best in the UnitedStates where the district level contests are dominated by only two politicalparties. To this extent, the suggestion that multi-partism would be the lessproximate cause of failure of party convergence in the SMD systems has someplausibility. But even in the United States the parties are not converging ascompletely as they apparently once did. In so far as the split in the Labour partyand the formation of the Social Democrats enhanced British ‘multi-partism’, itfollowed the sharp movement of the Labour party to the left, rather thanpreceded it. At an even larger level than we can here investigate, the changingfortunes in Britain of two-party domination, vote–seat disproportionality, anddivergence of the large parties from the citizen median from the 1950s through1997 seems to illustrate a volatility of representation in these systems for whichthe standard model in its current state of development remains insufficient.

CONCLUSION: EFFECTIVE THRESHOLDS, DISPROPORTIONALITY ANDREPRESENTATION

Our purpose in this article has been twofold. On the one hand, we wanted toreturn to a relationship that has been extensively studied by political scientistsinterested in electoral systems: the relationship between electoral systems anddisproportionality. Although it is well documented that less permissive electoralsystems, usually operationalized as systems with higher effective thresholds, areassociated with higher vote–seat distortion, the causal connection between thetwo is often underdeveloped. In the first part of this article, we tried to highlightsome of these connections in more detail. Surprisingly, doing so generated newinsights into the connection between vote–seat distortion and electoral systems.Most importantly, our emphasis on the importance of cross-district cancellationsuggested that high threshold systems do not necessarily lead to higherdisproportionality, but merely create the potential for it. However, theconditions necessary to reduce disproportionality are rather stringent. Accord-ingly, the average disproportionality as well as the variance of vote–seatdistortion is expected to be higher in high threshold systems. Our data wereindeed consistent with this hypothesis.

Part of the interest in the relationship between seats and votes, at leastimplicitly, derives from the assumption that the votes citizens cast revealsomething about their preferences. However, there are two problems with this


view. First, how citizens vote, and what choices they face (i.e. what partiescompete for office) is itself, at least in part, a product of the electoral system.Strategic voters and politicians can behave in ways that obscure the relationshipbetween preferences and votes; hence votes are imperfectly suited to measuringthe quality of preference representation.

A second problem with disproportionality as a measure of the quality ofrepresentation is that vote–seat disproportionality treats as equally serious allfailures of large parties to achieve legislative representation proportionate totheir voter support. But for theorists favouring a majoritarian approach todemocratic government, what matters for representation is whether the electedmajority in the legislature prefers policies favoured by a majority of the citizens.The majoritarian vision that underlies much justification of SMD electoralsystems holds explicitly that the point of elections is decisively to choose agovernment that can directly implement policies preferred by a majority ofcitizens and is highly accountable.44 Such decisiveness may well entailreduction in the range of represented views. What matters for representation isnot vote–seat proportionality, but whether the elected majority is representativeof what the majority of citizens want. Some vote–seat disproportionality mighthelp achieve this goal; other disproportionality might hinder it.

Both of these arguments suggest that it would be desirable to find more directmeasures of citizen preferences in an attempt to evaluate the quality ofrepresentation. In this article, we have suggested one particular measure, namelythe correspondence between the medians of citizen and legislative preferencedistributions on the left–right scale. The most important finding is that althoughthe measure of median correspondence is conceptually better suited forevaluating the quality of representation in SMD systems, these systems do notperform as well as PR systems under this criterion. We gained further confidencein this result, at least for this sample of elections, by examining several differentmeasures of party placements, including their published manifesto positions. Atleast empirically, PR systems seem to produce systematically closer cor-respondence between medians.

Cox’s suggestion that strategic failures, whether of voters or parties, should bemore costly for preference representation in the SMD systems does look remarkablyacute.45 The failure of parties to converge to the citizen median and/or to reducethe number of competitors to the carrying capacity of the electoral system can pulllegislative medians quite far from the citizens. In some of our PR systems, too, thereseem to be similar phenomena: parties near the median not getting the votes onewould expect (the Freie Demokratische Partei (F

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Election Laws, Disproportionality and Median Correspondence: Implications … · 2018. 7. 11. · 2 Consider Arend Lijphart’s judgement: ‘This is an important practical conclusion